Doping-driven evolution of pairing symmetry in pressurized La₃Ni₂O₇

Summary

Using a minimal bilayer two-orbital model and the random phase approximation, we investigate the superconducting pairing symmetry and its doping evolution in pressurized La₃Ni₂O₇. In the undoped system, the most favorable pairing state is an s± wave whose gap function changes sign between different Fermi pockets; the analysis indicates that this unconventional pairing arises from repulsive interactions mediated by the magnetic odd mode of the bilayer nickelate. Hole doping enlarges the γ Fermi pocket, and the intrapocket repulsion driven by the magnetic even mode gradually strengthens and dominates the pairing interaction, eventually driving the pairing symmetry from s± wave to dxy wave in the heavily hole-doped regime. In contrast, under electron doping the s±-wave pairing persists and remains stable even in the deeply electron-doped region where a Lifshitz transition occurs, indicating that the γ Fermi pocket is not a necessary condition for superconductivity in bilayer nickelates; owing to favorable nesting between the α and β pockets that enhances spin fluctuations, the s± wave becomes even more robust in the absence of the γ pocket. This study reveals the doping control of pairing symmetry and provides a new route for testing the superconducting pairing mechanism in pressurized La₃Ni₂O₇.

Materials

• La₃Ni₂O₇

Methods

• minimal bilayer two-orbital model
• random phase approximation
• spin susceptibility calculation
• charge susceptibility calculation
• pairing interaction decomposition
• linearized pairing gap equation

Keywords

• superconducting pairing symmetry
• s± wave pairing
• dxy wave pairing
• spin fluctuations
• magnetic odd modes
• magnetic even modes
• lifshitz transition
• fermi surface nesting
• hole doping
• electron doping

Highlights

• The work identifies magnetic odd modes as the microscopic mechanism responsible for the widely discussed s±-wave pairing in pressurized La₃Ni₂O₇, a connection that remained unclear in previous studies.
• A hole-doping-driven transition from s±-wave to dxy-wave pairing symmetry is predicted, providing a new route for testing the pairing mechanism.
• The gamma Fermi pocket is shown not to be a prerequisite for superconductivity, in contrast to proposals emphasizing its necessity.
• Complementary investigations of bilayer nickelate thin films and bulk samples are proposed to help unravel the microscopic pairing mechanism.

Conclusions

• For undoped pressurized La₃Ni₂O₇, the most favorable pairing state is s±-wave with sign reversal of the gap functions between the Fermi pockets.
• The s±-wave pairing state originates from repulsive interactions mediated by the magnetic odd modes of the bilayer nickelate.
• Hole doping expands the gamma Fermi pocket, enhances intrapocket repulsions driven by magnetic even modes, and drives a transition from s±-wave to dxy-wave pairing in the heavily hole-doped regime.
• Electron doping does not destroy s±-wave pairing, which persists even below the Lifshitz transition where the gamma pocket disappears.
• The gamma Fermi pocket is not essential for superconductivity in pressurized bilayer nickelates; favorable nesting between the alpha and beta pockets enhances spin fluctuations and stabilizes s±-wave pairing.

Main claims

• Undoped pressurized La₃Ni₂O₇ supports s±-wave pairing with sign reversal of the gap between Fermi pockets.
  • Evidence: Abstract: 'the most favorable pairing state is found to be s±-wave, characterized by sign reversal of the gap functions between the Fermi pockets',Full text: 'The dominate channel is the s±-wave pairing state… gap function is positive on the gamma pocket and negative on the alpha and beta pockets.'
• The s± pairing originates from repulsive interactions mediated by magnetic odd modes of the bilayer nickelate.
  • Evidence: Full text: 'the pair scatterings between bands of opposite parity arise from magnetic odd modes',Full text: 'Gammabeta gamma derives entirely from the odd modes of the magnetic excitations.'
• Hole doping drives a transition from s±-wave to dxy-wave pairing.
  • Evidence: Abstract: 'Upon hole doping… ultimately drive a transition in pairing symmetry from s±-wave to dxy-wave in the heavily hole-doped regime.',Full text: 'a transition in pairing symmetry from s±-wave to dxy-wave occurs upon hole doping. This transition is driven by the strong enhancement of the magnetic even modes induced by hole doping.'
• The gamma Fermi pocket is not essential for superconductivity, since s± pairing persists under electron doping and below the Lifshitz transition.
  • Evidence: Abstract: 'the s±-wave pairing persists under electron doping, even deep into the heavily electron-doped regime where a Lifshitz transition occurs.',Full text: 'The leading pairing state remains the s±-wave symmetry… even though the gamma pocket lies entirely below the Fermi level.'

Workflow

• model_setup — A minimal bilayer two-orbital model with on-site interactions is adopted to study pairing in pressurized La₃Ni₂O₇.
  • Materials: minimal bilayer two-orbital Hamiltonian; tight-binding hopping parameters from Ref. [41]; on-site interactions U, U', J, J'
  • Methods: define kinetic terms for Ni-dx2-y2 and Ni-d3z2-r2 orbitals in a bilayer lattice; impose rotational symmetry constraints U'=U-2J and J=J'
  • Observations: low-energy model includes alpha, beta, and gamma Fermi pockets; gamma pocket is associated with the Ni-d3z2-r2 orbital
• calculation — RPA calculations identify s±-wave as the dominant pairing symmetry for the undoped compound.
  • Materials: RPA spin and charge susceptibilities; spin-singlet pairing interaction matrix
  • Methods: compute bare and RPA spin/charge susceptibilities; construct singlet pairing vertex and project onto band representation; diagonalize pairing matrix to obtain pairing eigenvalues and gap functions
  • Observations: leading channel is s±-wave with positive gap on gamma pocket and negative gap on alpha and beta pockets; subdominant d-wave channels are nearly degenerate at weak interaction
• analysis — Magnetic odd modes drive the undoped s± pairing, while magnetic even modes become dominant under hole doping.
  • Materials: momentum-resolved pairing interactions Gammaalpha beta, Gammaalpha gamma, Gammabeta gamma, Gammagamma gamma; parity decomposition of spin-fluctuation-mediated pairing vertex
  • Methods: examine Fermi-surface angle dependence of pairing interactions; relate interband pair scattering to magnetic odd/even modes using band parity
  • Observations: dominant interpocket repulsions Gammabeta gamma and Gammaalpha gamma arise from magnetic odd modes; hole doping enhances intrapocket Gammagamma gamma from magnetic even modes; electron doping enhances Gammaalpha beta through alpha-beta nesting
• interpretation — The gamma Fermi pocket is not essential for superconductivity; doping controls the pairing symmetry of pressurized La₃Ni₂O₇.
  • Materials: doping-dependent Fermi surface topology; Luttinger theorem constraint
  • Methods: compare hole-doped and electron-doped pairing eigenfunctions; track Lifshitz transition of the gamma pocket
  • Observations: hole doping changes leading pairing from s± to dxy; electron doping preserves s± even when the gamma pocket is absent below the Lifshitz transition; spin fluctuations strengthen due to alpha-beta nesting when gamma pocket vanishes